Arranging Dissimilar Fractions Lesson 61 Objective Arrange dissimilar

Arranging Dissimilar Fractions Lesson 61

Objective Arrange dissimilar fractions in increasing or decreasing order. Math 3

Drill four-fourths five-fourths seven-sixths four-thirds 4 7 1 3 7 6 one-third 7 10 4 4 5 4

4 3 8 8 2 7 3 5 foursevenths two-sevenths three-fifths eight-eights seven-tenths

Review “Fractions less than One” “Fractions more than One” “Fractions Equal to One” Math 3

Place the fractions in their appropriate column. Ask a pupil to get a pair of fractions, e. g. 1 and 2 and 3 7 compare them. Call about 3 more pupils to compare a pair of functions Math 3

Motivation Have you experienced going to the market? What products do you usually buy in the market? Math 3

Check ( ) on your show -me-board if the item is sold in the market and cross ( ) if. Xthe item is sold in the hardware. Math 3

fruits nail Math 3

chicken vegetables wood Math 3

Presenting the Lesson Kathleen and her mother went to the market. She helped her in buying the following ingredients: Math 3

3/4 kilogram of chicken 1/2 kilogram of sayote 1/8 kilogram of ginger 1/4 kilogram of onions Math 3

What recipe do you think Kathleen’s mother plans to cook? Do you also help your mother at home? How? What household chores do you do to help your mother?

If we are going to arrange the ingredients from lightest to heaviest, which should come first? second? third? fourth? Why?

Performing the Activities Drawing Method 3/4 kilogram of chicken 1/2 kilogram of sayote Math 3

1/8 kilogram of ginger 1/4 kilogram of onions Let us use some drawings to represent the weight of each ingredient. Math 3

3/4 kilogram of chicken 1/2 kilogram of sayote 1/8 kilogram of ginger 1/4 kilogram of onions Math 3

From the drawing, which one is the lightest? heaviest? How will you arrange the fractions from lightest to heaviest? heaviest to lightest? Answer: lightest to heaviest – 1/8, 1/4, 1/2, 3/4 heaviest to lightest – 3/4, 1/2, 1/4, 1/8 Math 3

Aside from using drawing, how else can we determine the value of dissimilar fractions so that we can arrange them in increasing order. (By changing them to similar fractions) Math 3

Least Common Denominator (LCD) Method How do we change dissimilar to similar fractions? Math 3

Step 1: Find the LCD of the denominators. The LCD is the least common multiple of the denominators. 2: 2, 4, 6, 8, … 4: 4, 8, 12, 16, … 8: 8, 16, 24, 32, … Math 3

What is the LCD of 2, 4, & 8? (8) Math 3

Step 2: Change the fractions with 8 as their common denominators. Divide the LCD by the denominator, then, multiply the quotient by the numerator. The product becomes the new numerator. Math 3

X 3 6 = 4 ÷ 8 2 X 1 4 = 2 ÷ 8 4 8 ÷ 4 = 2; 2 X 3 = 6 So, 3 = 6 4 8 8 ÷ 2 = 4; 4 X 1 = 4 So, 1 = 4 2 8 Math 3

X 1 1 = 8 ÷ 8 1 X 1 2 = 4 ÷ 8 2 8 ÷ 8 = 1; 1 X 1 = 1 So, 1 = 1 8 8 8 ÷ 4 = 2; 2 X 1 = 2 So, 1 = 2 4 8 Math 3

So, what are the fractions equivalent to 3/4, 1/2, 1/8 and 1/4 so that their denominators are the same? 3= 6 4 8 1= 4 2 8 1= 1 8 8 1= 2 4 8 Math 3

For similar fractions, the bigger the numerator, the greater the fraction. So the fraction with the biggest numerator is 6/8. Followed by 4/8, then, 2/8, and lastly 1/8.

If we arrange the dissimilar fractions changed to similar fractions, the arrangement in increasing order will be 1/8, 1/4, 1/2, 3/4.

There is another way to find the similar fractions of dissimilar if the LCD is already found. 3 X 2= 6 What will you multiply 4 2 8 8 to 4 to get 8? Multiply the number you used in the denominator to the numerator. What did you get?

1 X 4= 4 What will you multiply 2 4 8 8 to 2 to get 8? Multiply the number you used in the denominator to the numerator. What did you get?

1 X 1= 1 I/8 is already in 8 1 8 8 eighths, so it will be the same. 1 X 2= 2 What will you multiply 4 2 8 8 to 4 to get 8? Multiply the number you used in the denominator to the numerator. What did you get?

1/5 1/2 1/4 1/3

Looking at the shaded parts, we can arrange the fractions in descending order (from greatest to least). Which will be the first one, second, third and last? 1/2, 1/3, 1/4, 1/5

What have you noticed with the set of fractions? What can you say about the numerators? denominators? What happens to the fraction as the denominator increases?

Can we arrange the fractions even without illustrations? How will you do it? How will you arrange the fractions in ascending order(least to greatest)?

Which fraction will be the first? second? third? last? What have you noticed as you arrange them in ascending order? Which fraction became first? last?

To order fractions with the same numerators (unit fractions), compare their denominators, the greater the denominator of the fraction, the lesser the fraction.

Reinforcing the Concept Group Activity A. 5/6, 4/8, 3/4, 1/5 B. 2/8, 3/10, 1/2, 3/5 C. 1/5, 1/10, 1/2 , 1/7 D. 3/11, 15/11, 9/11, 5/11 Math 3

Gawain 1: Paghambingin ang mga dissimilar fraction sa bawat pangkat at ayusin ang mga ito mula sa pinakamaliit hanggang sa pinakamalaki. Isulat ang sagot sa inyong papel.

Answer Key: 1. ) 1/6, 1/5, 1/3, 1/2 2. ) 1/2, 2/3, 3/4, 4/5 3. ) 7/5, 7/4, 7/3, 7/2 4. ) 1/2, 5/8, 2/3, 3/4 5. ) 1/6, 1/4, 2/3, 7/8

Gawain 2: Ayusin ang pangkat ng dissimilar fraction sa ibaba mula sa pinakamalaki hanggang sa pinakamaliit. Isulat ang sagot sa inyong papel. Isulat ang sagot sa inyong kwaderno.

Answer Key: 1. ) 1/2, 2/5, 1/8 2. ) 5/6, 3/4, 4/8 3. ) 5/3, 5/6, 5/12 4. ) 7/9, 2/3, 1/2 5. ) 7/2, 7/3, 7/4

Summarizing the Lesson How do we arrange a set of fractions in increasing or decreasing order?

a. Unit Fractions To order/arrange fractions with the same numerators but different denominators, compare their denominators. The greater the denominator of the fraction, the lesser the fraction.

b. Dissimilar Fractions To order/arrange fractions with the different numerators and denominators, we change them first to similar fractions by finding the LCD of the denominators. Then, rename the fractions to its equivalent using the LCD.

When all fractions are already renamed with the same denominators, the numerators can be now compared: • the greater the numerator, the greater the value of the fraction. • the lesser the numerator, the lesser the value of the fraction.

Applying to New and Other Situations Group Activity Note: fractions should be written in a card with string/yarn so that they can wear it like an ID.

5 9 5 4 5 11 5 3 Math 3

2 3 1 9 5 6 4 12 Math 3

2 5 3 4 1 2 4 10 Math 3

1 8 3 2 2 4 5 6 Math 3

2 5 2 9 2 7 2 3 Math 3

Gawain 3 Magbigay ng fraction na nasa pagitan ng pares ng fraction sa bawat bilang. Gawin ito sa inyong sagutang papel.

Possible Answers: 1. ) 5/6 2. ) 3/4 3. ) 1/2 4. ) 5/10 5. ) 1/2

Evaluation: Gawain 4 Gamitin ang mga sumusunod na fraction upang masagot ang bawat tanong. 2, 3, 1, 3 5 4 6 9 Math 3

1. ) Kung aayusin ang pangkat ng fraction na ito mula sa pinakamaliit, aling fraction ang: a. ) una? ______ b. ) huli? ______ Math 3

2. ) Kung aayusin ang pangkat ng fraction na ito mula sa pinakamalaki, aling fraction ang: a. ) una? ______ b. ) huli? ______ Math 3

3. ) Ayusin ang pangkat ng fraction a. ) Pinakamaliit hanggang sa pinakamalaki b. ) Pinakamalaki hanggang sa pinakamaliit Math 3

Key Answer: 1. ) a. )1/6, b. ) 3/4 2. ) a. ) 3/4, b. ) 3/9 3. ) a. ) 1/6, 3/9, 2/5, 3/4 b. ) 3/4, 2/5, 3/9, 1/6 Math 3

Takdang Aralin: Gawain 5 Isinulat ni Aling Rosa ang pinamili ng lima niyang customer. Basahin at pag-aralan ang talaan na ginawa ni Aling Rosa. Math 3

Mami mili Kamat Sibuy Bawan Patata is as g s Vicky 1 kg 2 4 kg 5 Letty 2 kg 3 1 kg 8 1 kg 4 2 kg 5 Math 3

Beth 3 kg 4 4 kg 6 1 kg 3 1 kg 2 Maria 1 kg 2 1 kg 8 1 kg 4 1 kg 3 Anne 3 kg 8 1 kg 4 1 kg 2 3 kg 4 Math 3

1. Ayusin ang pinamili ni Vicky mula sa pinakakaunti hanggang sa pinakamarami. 2. Ayusin ang pinamili ni Letty mula sa pinakamabigat hanggang sa pinakamagaan. 3. Alin sa mga pinamili ni Beth ang pinakamabigat? Pinakamagaan? Math 3

4. Ano ang binili ni Maria na pinakamabigat? pinakamagaan? 5. Kung aayusin mo ang mga pinamili ni Anne mula sa pianakamagaan hanggang sa pinakamabigat, anong fraction ang magiging ikatlo sa hanay? Math 3

Answer Key: 1. ) 1/4 kg, 1/2 kg, 4/5 kg 2. ) 2/3 kg, 2/5 kg, 1/8 kg 3. ) tomato is the heaviest 3/4 kg; garlic is the lightest 1/3 kg 4. ) onion is the lightest; tomato is the heaviest 5. ) 1/2 kg

Equivalent Fractions Lesson 62

Objective Visualize and generate equivalent fractions. Math 3

Drill 8 X 6 5 X 9 9 X 8 12 X 6 12 X 4 Math 3

6√ 42 12√ 24 8√ 64 7√ 56 9√ 54 Math 3

Review Write >, < or = on their show-meboard. Math 3

2 3 4 7 1 2 5 8 3 5 4 5 1 8 4 8 2 9 2 5

5 3 4 3 3 9 4 3 2 7 4 7 1 3 2 5 4 3

Motivation Carol and Tess are working together on their art project. Carol colored 1/2 of the square, while Tess colored 4/8 of another square of the same size. Tess told Carol that she colored more parts and has a bigger fraction. Carol said that they just have equal parts. Who is right?

Why are Carol and Tess busy? What are they doing? What kind of pupils are they? Do you also do your projects? Why is it better if you do a project together with a classmate? How many parts were colored by Carol? What about Tess? Who do you think is right? Carol or Tess?

Presenting the lesson Carol’s Project Tess’ Project Math 3

How many parts were colored by Carol? What do you call the shaded part? What about Tess colored part? What do you call the shaded part? How will you be sure that the two shaded parts are equal? Math 3

Is 1/2 equal to 4/8? How can we check if 2 fractions are equivalent fractions? What kind of fractions are 1/2 and 4/8? Equivalent Fractions Math 3

Presenting the lesson Can you think of another fractions equivalent to 1/2 and 4/8?

A. B. What part of the whole is shaded in Square A? 2/4

What about in Square B? 3/6 Are the two fractions equal? Are they also equal to 1/2? Are the products of the fractions equal?

2 4 3 6 2 X 6 = 12 4 X 3 = 12 If the product of 2 and 6 is the same with the product of 4 and 3 then the 2 fractions are equivalent.

Are the fractions 2/4, 3/6 and 3/6 equals to 1/2? How can we generate fractions equivalent to a given fraction?

1=2, 3, 4 2 4 6 8 What have you noticed with the series of fractions? How can we get 2/4 from 1/2? What will you do to the numerator and denominator of 1/2 to 3/6? 4/8? Math 3

6=3, 2, 1 18 9 6 3 How can we get 3/9 as equivalent fraction to 6/18? What will you do to the numerator and denominator of the fraction? Math 3

To generate fractions equivalent to a given fraction, we can either multiply or divide both the numerator and denominator of the given fraction by the same whole number. Math 3

Let us try to check the equivalent fractions we have formed. 1 2 1 x 2 = 2 , 1 x 3 = 3, 2 x 2 4 2 x 3 6 1 x 4 =4 2 x 4 8 Math 3

2 3 2 x 2 = 4 , 2 x 3 = 6, 3 x 2 6 3 x 3 9 2 x 4=8 3 x 4 12 2=4, 6, 8 3 6 9 12 12 24 12÷ 2 = 6 , 12÷ 3 = 4, 24÷ 2 12 24÷ 3 8 12 = 6 , 4 , 3 24 12 8 6 12÷ 4 = 3 24÷ 4 6 Math 3

Is there another way to find equivalent fractions of a given fraction? Math 3

1 whole 1/2 1/3 1/4 1/4 1/5 1/5 1/5 1/6 1/6 1/6 1/8 1/8 1/10 1/10 1/10 1/12 1/12 1/12

Can you form equivalent fractions for 1/4? What fractions are as big as 1/4? So 2/8 and 3/12 is equivalent to 1/4? Can you see other equivalent fractions from the chart?

Multiple Chart There is another way of getting the equivalent of a fraction. Study the number chart.

1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 32 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 20 30 40 50 60 70 80 90 100

Look at the shaded part in the number chart. Based on the number chart consider the numbers above as the numerators and the numbers below are the denominators. See if all the fractions following 1/2 are its equivalent. Are they? Math 3

1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 What about 3/4? Can you see its equivalent fractions? Math 3

Processing the Activities How do you know that 2 fractions are equivalent/equal? What can you say about the parts or values of equivalent fractions? How will you form equivalent fractions?

Reinforcing the Concept Group Activity Note: Fractions should be written in a card with string so that they can wear it like an ID. Math 3

5 6 10 12 15 18 20 24 25 30 Math 3

3 4 6 8 9 12 12 16 15 20 Math 3

1 2 7 14 5 10 3 6 10 12 Math 3

2 5 6 15 10 25 4 10 12 30 Math 3

2 3 6 9 10 15 14 21 4 6 Math 3

Gawain 1 Ibigay ang katumbas na fraction ng mga figure na nasa ibaba. Isulat ito sa sagutang papel. Math 3

1. 2 8 = Math 3

2. 3 5 = Math 3

3. 4 8 = Math 3

4. 1 3 = Math 3

5. 3 3 = Math 3

6. 3 5 = Math 3

Answer Key: 1. ) 1/4 4. ) 2/6 2. ) 6/10 5. ) 2/2 3. ) 3/6 6. ) 8/16 Math 3

Gawain 2 Kopyahin sa inyong kwaderno ang gawain. Buuin ang pares ng magkatumbas na fraction. Gamitin ang cross product para makuha ang nawawalang numerator at denominator. Math 3

1. 3 = 9 27 4. = 2 15 3 2. 2 = 5 45 5. 2 = 4 4 3. 45 = 5 81 6. 5 = 25 5 Math 3

Answer Key: 1. 9 4. 10 2. 18 5. 8 3. 9 6. 1 Math 3

Summarizing the Lesson How do you define equivalent fractions? Equivalent fractions are fractions that name or describe the same part of a region or set. They have the same value but different numerators and denominators. Math 3

How will you determine if two fractions are equivalent fractions? Use the cross product method. If their cross products are the same, then the 2 fractions are equivalent. Math 3

How can we generate equivalent fractions? To get the equivalent of a given fraction, we can either multiply or divide the number and the denominator by the same number. Math 3

Divide the class into 5 groups. Let them choose their leader. Give to the leader a card with fraction written on it. Tell them to form 3 or 4 fractions equivalent to the given fraction to the group leader. Let them write their answer on 1/2 sheet of cartolina and post their work on Applying to New and the board. The leader will report to Other Situations the class about their work. Math 3

Gawain 3 Tingnan ang fraction sa kaliwa at magbigay ng tatlong fraction na katumbas nito. Isulat ang sagot sa sagutang papel. Math 3

1. 5 6 2. 26 52 Math 3

3. 2 11 4. 5 4 5. 42 56 Math 3

Possible Answers: 1. ) 10/12, 15/18, 20/24 2. ) 1/2, 2/4, 3/6 3. ) 4/22, 6/33, 8/44 Math 3

4. ) 10/8, 15/12, 20/16 5. ) 6/8, 3/4, 9/12 Math 3

Evaluation Gawain 4 Sipiin sa inyong kuwaderno kung alin sa sumusunod na pares ng fraction ang magkapareho o magkatumbas. Bilugan ang pares ng fraction na magkatumbas. Math 3

1. ) 1 , 1 4 8 2. ) 3 , 6 5 10 3. ) 15 , 3 20 4

4. ) 1 , 5 5 25 5. ) 4 , 8 5 15

Answer Key: 2. ) 3/5, 6/10 4. ) 1/5, 5/25 3. ) 15/20, 3/4 Math 3

Takdang-Aralin Gawain 5 Kopyahin ang gawain sa sagutang papel. Bilugan ang pangkat ng fraction na magkatumbas. Math 3

1. ) 4 , 6 , 8 5 8 10 2. ) 6 , 4 , 3 14 8 7 3. ) 1 , 3 , 6 3 9 8

4. ) 5 , 10 6 18 18 5. ) 4 , 6 , 8 18 27 36 6. ) 2 , 6 , 4 3 9 10

B. Tingnan ang pattern sa ibaba. Buuin ang mga nawawalang bilang sa pamamagitan ng pagsulat ng mga katumbas na fraction sa bawat bilang. Math 3

4. ) 1 , 2 , 3 , __ 5 10 15 5. ) 1 , 2 , 3 , __ 10 20 30

Answer Key: A. 1. ) 4 , 8 5 10 4. ) 5 , 15 6 18 2. ) 6 , 3 14 7 5. ) 6 , 8 27 36 3. ) 1 , 3 3 9 6. ) 2 , 6 3 9 Math 3

B. 1. ) 4/8, 5/10, 6/12 2. ) 4/12, 5/15, 6/18 3. ) 4/16, 5/20, 6/30 4. ) 4/20, 5/25, 6/30 5. ) 4/40, 5/50, 6/60 Math 3

Point, Line Segment and Ray Lesson 63

Objective Recognize and draw a point, line segment and ray. Math 3

Drill Get objects from the room. Identify the objects and describe the shape of the object.

Review Gawain 1 Kumpletuhin ang puzzle sa tulong ng mga gabay na tanong sa ibaba. Math 3

2 1 3 4 Math 3

1. Hugis ng may apat na gilid o side at may magkabilang gilid na magkasinghaba o parallel sides. 2. Saradong hugis na walang gilid o side.

3. Hugis na may tatlong gilid o side. 4. Hugis na may apat na gilid o side na magkaparehong haba.

Answer Key: 1. Rectangle 3. Triangle 2. Circle 4. Square

Motivation Points and lines That’s how it starts Making all the figures Using points and lines Points and lines. Math 3

What does it tell? Where do figures come from as described in the poem? Today, you are going to study about points and lines. Math 3

Presenting the Lesson David and Vince are playing darts. Look at where their darts landed. David Vince Math 3

What did David and Vince name the space/place where their darts landed? How will you describe the figure where the darts landed? How many points are marked? If you play darts, what would you like to name your point? How are points named? Math 3

A dot represents a point. It can be named with letters. Look at the picture. R S T Math 3

What have you noticed from point R to point T? What can you see at both ends? What do you call this figure? This figure with two arrow heads is called a line. It can extend indefinitely in both directions. Math 3

Look at the example below. Take a part of line RT. R S 1 T 2 Math 3

What do you call the figure below? How will you describe this figure? S T Math 3

This figure is called a ray. It has one end point and an arrow head which extends indefinitely to one direction. Start naming the ray from the endpoint. How many rays are there in line RT? Math 3

Look at the picture. Tell something about it. A B C D Math 3

Look at the part of the line from point B to point C. What can you say about this part? Can you call this part as ray? Why? Math 3

This figure is called a line segment. It has two end points. It can never extend indefinitely to any direction. Look around the classroom and find examples of each geometric figure discussed. Math 3

Performing the Activity Gawain 2 Tingnan ang figure at tukuyin ang mga ray na makikita dito. Math 3

H G I J Math 3

1. Tukuyin ang mga line segment na makikita sa figure. R E M Y Math 3

2. Sabihin ang mga linya (line) na makikita sa figure. N P Q O Math 3

Answer Key: 1. ) GH, GI , GJ 2. ) RE, EY, MY, RM 3. ) NO, PQ

Processing the Activities What do we call each figure below? How do you describe these figures? a. c. b. d.

Reinforcing the Concept Gawain 3 Punan ng tamang salita ang patlang upang mabuo ang pangungusap. Isulat ang sagot sa inyong sagutang papel.

1. Ang _____ ay may dalawang arrow head sa magkabilang dulo. 2. Ang _____ ay figure na may isang endpoint at arrow head.

3. Ang _____ ay may dalawang endpoint. 2. Ang _____ ay maaaring pangalanan ng letra.

Answer Key: 1. ) line 2. ) ray 3. ) line segment 4. ) point

Summarizing the Lesson What is a point? line segment? ray?

• A dot represents a point. It can be named with letters. • A figure with two arrow heads is called a line. It can extend indefinitely in both directions.

• A line segment has two end points. It can never extend indefinitely to any direction. • A ray has one end point and an arrow head which extends indefinitely to one direction.

Applying to New and Other Situations Gawain 4 Tingnan ang figure sa ibaba at sagutin ang mga tanong saa bawat bilang. M N O P

1. ) Magbigay ng pangalan ng point. 2. ) Sabihin ang pangalan ng linya (line).

3. ) Magbigay ng tatlong line segment. 2. ) Isa-isahin ang ray na makikita sa figure.

Answer Key: 1. ) Points M, N, O, and P 2. ) MP 3. ) MN, MO, MP, NO, NP, OP 4. ) MP, NP, OP, PM, OM, NM

EVALUATION Gawain 5 Isulat ang titik ng tamang sagot sa sagutang papel.

1. Ang tuldok o dot ay kumakatawan sa _______ A. Line B. Ray C. Point D. Line Segment

2. Ang _______ ay maaring lumawig nang walang katapusan sa magkabilang direksyon. A. Point B. Line C. Segment D. Dot

3. Ang ray ay bahagi ng linya na binubuo ng isang endpoint at _______. A. Arrowhead B. Endpoint C. Line D. Dot

4. Ang line segment ay bahagi rin ng linya na may _______ endpoint. A. 1 B. 2 C. 3 D. 4

5. Ang simbolong ito ay kumakatawan sa _______. A. Segment B. Ray C. Line D. Point

Answer Key: 1. c 2. b 3. a 4. b 5. c Math 3

Takdang Aralin Gawain 6 1. ) Gumuhit ng line segment upang makabuo ng Christmas star. Lagyan ng pangalan ang line segment na iginuhit mo.

2. ) Gamit ang mga letra, bigyan ng pangalan ang mga points, line, at ray na makikita sa figure sa ibaba.

Name of points, lines, and rays vary depending upon the letters the pupils will use. Sagot Math 3